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Showing papers on "Modal operator published in 1969"


Journal ArticleDOI
01 May 1969-Noûs
TL;DR: In this paper, the basic concepts of modal logic are presented from a philosophical perspective, both philosophical and formal, and the aim of this paper is to present a certain philosophical perspective.
Abstract: The aim of this paper is to present a certain philosophical perspective on the basic concepts of modal logic. The essentials of our approach, both philosophical and formal, are found in a previous paper,2 but will be recounted briefly in sections 1 and 3. Section 2 contains an intuitive explanation of our interpretation of the modal operators, and section 4 its formal counterpart. Section 5 considers quantification and singular terms in modal contexts. In section 6 we return to philosophical issues with the question whether t-he interpretation of modal language involves metaphysical commitments.

23 citations


Book ChapterDOI
01 Jan 1969
TL;DR: A system of modal logic is sketched in which modal operators are relativised to individuals or sets of individuals, suggested by certain expressions in ordinary language.
Abstract: In this paper I shall sketch a system of modal logic in which modal operators are relativised to individuals or sets of individuals. This extension of modal logic is suggested by certain expressions in ordinary language. For example, under certain circumstances we may utter the sentence (A) John can catch the trainwhich may be taken to be equivalent to (A’) It is possible for John to catch the train.

18 citations



Journal ArticleDOI
TL;DR: In this paper, it was shown that where S is modal LPC + S5 + Pr 2 then de re modalities are not eliminable in S. Theorem 1.
Abstract: A formula α of modal LPC is a de re modality iff it contains a free individual variable within the scope of a modal operator; otherwise α is de dicto . 1 We shall say that de re modalities are eliminable in a system S of modal LPC iff there is a transformation R on wffs of S such that R(α) is de dicto and ├ s α ≡ R(α) . We shall show that where S is LPC + S5 + Pr 2 then de re modalities are not eliminable in S.

6 citations



Book ChapterDOI
01 Jan 1969
TL;DR: The Lewis systems of modal logic S1–5 are treated as formalizations of the notion of implication rather than of possibility and necessity, and there is good evidence that Lewis would approve of the treatment of his systems.
Abstract: The Lewis systems of modal logic S1–5 were originally constructed as N-K-M systems, i.e. with the help of primitive operators for negation (N), conjunction (K) and possibility (M). As a result they are normally considered as strengthenings of classical two-valued logic (PC), since the axioms and rules of inference of PC are easily derivable in even the weakest of them. If, however, S1–5 are reformulated as C-N-K systems in which the primitive operator C of strict implication replaces M (the latter then being definable via the definition Mα = NCαNα), the Lewis systems appear in quite a different light. Since every thesis which holds of strict implication holds also of material implication (but not vice versa), S1–5 emerge as progressively stricter fragments of PC rather than as containing it. Furthermore, they are then properly speaking systems of propositional logic rather than systems of modal logic, though of course the modal operators L and M are definable in them, and their characteristic modal theses derivable. Although Lewis (with an assist from Hugh MacColl) is the founder of modern modal logic, there is good evidence that he himself preferred to regard the Lewis systems as formalizations of the notion of implication rather than of possibility and necessity: furthermore, the notion of implication Lewis had in mind was arrived at by restricting and so to speak cutting some of the fat off material implication. Hence Lewis would approve of the treatment of his systems in this paper.

3 citations


Journal ArticleDOI
TL;DR: In this article, some bi-modal systems involving two kinds of modal operators are constructed in Gentzen-type formulations with the proof of the Hauptsatz for some of these systems.
Abstract: In this paper some bi-modal systems involving two kinds of modal operators are constructed in Gentzen-type formulations with the proof of the " Hauptsatz " for some of these systems.